# Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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1answer
35 views

### How to compute for a sequence for a given value in wolfram?

What would be the correct input in the wolfram website to give u(n) for a given n, where u is a sequence ? Something like: ...
1answer
49 views

### Calculating the 1st quartile: different result with Excel, Wolfram Alpha and using formula in my math book - why?

I have the following set of numbers: 1, 1, 8, 12, 13, 13, 14, 16, 19, 22, 27, 28, 31 I'm supposed to calculate the value of the 1st quartile (25th percentile) in this data set. Using the formula in ...
1answer
58 views

2answers
65 views

### How do I solve a recurrence relation with multiple conditions?

Suppose I have a recurrence relation like : \begin{equation} f(n)=\begin{cases} 2*f(n-1) , & \text{n%2 = 1}.\\ f(n-1) + 1, & \text{n%2 = 0}. \end{cases} \end{equation} \begin{...
0answers
61 views

### Wrong Wolfram alpha result on $nth$ derivative?

I'm working with this function $$f(x)=\left(x+\sqrt{x^2-a}\right)^{-b}$$ and I would like to know the $nth$ derivative of $f(x)$. To this end, I ask Wolfram alpha about that given me the following ...
1answer
35 views

### Is there some technique to plot complex functions by hand?

Is there some technique to plot complex functions by hand? Particularly, consider e.g. $$x=\exp(t)\cos(t), y=\exp(t)\sin(t)$$ This is equivalent to $e^x(\cos(y)+i\sin(y))$ along line $y=x$, just ...
0answers
30 views

### Why do these Residues and Numerically Calculated Contour Integrals Disagree?

I've been trying to numerically approximate various contour integrals of the function $f(z)=\frac{\sin\left(\pi x\right)}{\sin^2\left(\frac{15\pi}{x}\right)}$, but it seems that the residues and ...
1answer
103 views

0answers
23 views

### Calculating an area of parametric function with wolframalpha?

Using wolframalpha, how can I calculate an area between some parametric function like: $\begin{cases} x(t) = t^2 - t \\ y(t) = t^3\end{cases}$ and: some other function like: $y = x^2$ ? I've ...
2answers
57 views

### How to find $\frac{146}7 \mod{7}$?

I understand that if $\gcd{(b,c)}=1$ then we can find $\frac{a}b\mod{c}$ by writing $$x\equiv \frac{a}b\mod{c}$$ $$bx\equiv a\mod{c}$$ then reducing $a$ and solving the modular equation by finding the ...
3answers
50 views

### How to compute $a\cdot \lim\limits_{n \to \infty}n?$

How to compute $$a\cdot \lim_{n \to \infty}n?$$ I think such an expression is not valid. Though $\lim\limits_{n \to \infty}n=\infty$, which is not a concrete real number, we can not put it into a ...
1answer
153 views

### Why wolfram alpha claimed that this $\sum_{n=1}^{\infty}\sin (\frac{n}{\sqrt{n!}})$ is converge by test and in the same time is diverge?

I'm confused why wolfram alpha claimed that this sum $$\sum_{n=1}^{\infty}\sin \left(\frac{n}{\sqrt{n!}}\right)$$ is convergent by test criterion, and in the same time is divergent in result below ...
1answer
79 views

0answers
75 views

### How to generate interpolating polynomial using Newton formula for exponential function?

I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0\ and\ x_3 = x_4 = 1$ with Newton's formula using Wolfram Alpha, but I am stuck with division ...
1answer
94 views

### Why does Wolfram Alpha give $\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$?

When I input $$\sum_{n=1}^{\infty}(e^i)^{n^2}$$ in Wolfram Alpha, it gives me the result, $$\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$$ I think this is wrong, but I do not understand why ...
1answer
107 views

### Global extrema for $\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$?

Does the function $$\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$$ have either a global minimum or a global maximum for $q \geq 5$ and $k \geq 1$? WolframAlpha is unable to find any. ...